Regularization Approaches for High‐Dimensional Cox Models: A Case Study in Triple‐Negative Breast Cancer

Summary In high‐dimensional survival analysis, effective variable selection is crucial both for model interpretation and predictive performance. This paper investigates Cox regression with lasso and adaptive lasso penalties in genomic datasets where covariates far outnumber observations. We propose and evaluate four weight calculation strategies for adaptive lasso specifically designed for high‐dimensional settings: ridge regression, principal component analysis (PCA), univariate Cox regression and random survival forest (RSF)‐based weights. To address the inherent variability in high‐dimensional model selection, we develop a robust procedure that evaluates performance across multiple data partitions and selects variables based on a novel importance index. Extensive simulation studies demonstrate that adaptive lasso with ridge and PCA weights significantly outperforms standard lasso in variable selection accuracy while maintaining similar or better predictive performance across various correlation structures, censoring proportions (0% to 80%) and dimensionality settings. These improvements are particularly pronounced in highly censored scenarios, making our approach valuable for real‐world genetic studies with limited observed events. We apply our methodology to triple‐negative breast cancer data with 234 patients, over 19 500 variables and 82% censoring, identifying key genetic and clinical prognostic factors. Our findings demonstrate that adaptive lasso with appropriate weight calculation provides more stable and interpretable models for high‐dimensional survival analysis.